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btree.py
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btree.py
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#!/usr/bin/env python
class BTreeNode:
def __init__(self, t, leaf, n):
self.leaf = leaf
self.n = n
self.t = t
self.key = [0] * (2 * t - 1)
self.c = [0] * (2 * t)
def split_child(self, i):
y = self.c[i - 1]
t = y.t
z = BTreeNode(t, y.leaf, t - 1)
for j in range(1, t):
z.key[j - 1] = y.key[j + t - 1]
if not y.leaf:
for j in range(1, t + 1):
z.c[j - 1] = y.c[j + t - 1]
y.n = t - 1
for j in range(self.n + 1, i, -1):
self.c[j] = self.c[j - 1]
self.c[i] = z
for j in range(self.n, i - 1, -1):
self.key[j] = self.key[j - 1]
self.key[i - 1] = y.key[t - 1]
self.n = self.n + 1
def insert_nonfull(self, k):
i = self.n
t = self.t
if self.leaf:
while i >= 1 and k < self.key[i - 1]:
self.key[i] = self.key[i - 1]
i = i - 1
self.key[i] = k
self.n = self.n + 1
else:
while i >= 1 and k < self.key[i - 1]:
i = i - 1
i = i + 1
if self.c[i - 1].n == 2 * t - 1:
self.split_child(i)
if k > self.key[i - 1]:
i = i + 1
self.c[i - 1].insert_nonfull(k)
def search(self, k):
i = 1
while i <= self.n and k > self.key[i - 1]:
i = i + 1
if i <= self.n and k == self.key[i - 1]:
return self, i
elif self.leaf:
return None
else:
return self.c[i - 1].search(k)
def print_inorder(self):
if self.leaf:
for i in range(1, self.n + 1):
print(self.key[i - 1], )
else:
for i in range(1, self.n + 1):
self.c[i - 1].print_inorder()
print(self.key[i - 1], )
self.c[self.n].print_inorder()
def print_child_first(self):
if not self.leaf:
for i in range(1, self.n + 2):
self.c[i - 1].print_child_first()
for i in range(1, self.n + 1):
print(self.key[i - 1], )
def delete(self, tree, k):
t = self.t
i = 1
while i <= self.n and k > self.key[i - 1]:
i = i + 1
if i <= self.n and k == self.key[i - 1]:
if self.leaf:
for j in range(i, self.n):
self.key[j - 1] = self.key[j]
self.n = self.n - 1
else:
y = self.c[i - 1]
z = self.c[i]
if y.n >= t:
p = y
while not p.leaf:
p = p.c[p.n]
key = p.key[p.n - 1]
y.delete(tree, key)
self.key[i - 1] = key
elif z.n >= t:
s = z
while not s.leaf:
s = s.c[0]
key = s.key[0]
z.delete(tree, key)
self.key[i - 1] = key
else:
self.merge(tree, i)
y.delete(tree, k)
elif self.leaf:
return None
elif self.c[i - 1].n <= t - 1:
if i <= self.n and self.c[i].n >= t:
a = self.c[i - 1]
b = self.c[i]
a.key[a.n] = self.key[i - 1]
self.key[i - 1] = b.key[0]
for j in range(2, b.n + 1):
b.key[j - 2] = b.key[j - 1]
a.c[a.n + 1] = b.c[0]
for j in range(1, b.n + 1):
b.c[j - 1] = b.c[j]
a.n = a.n + 1
b.n = b.n - 1
a.delete(tree, k)
elif i == self.n + 1 and self.c[i - 2].n >= t:
b = self.c[i - 2]
a = self.c[i - 1]
for j in range(1, a.n + 1):
a.key[j] = a.key[j - 1]
a.key[0] = self.key[i - 2]
self.key[i - 2] = b.key[b.n - 1]
for j in range(1, a.n + 2):
a.c[j] = a.c[j - 1]
a.c[0] = b.c[b.n]
b.n = b.n - 1
a.n = a.n + 1
a.delete(tree, k)
elif i <= self.n:
self.merge(tree, i)
self.c[i - 1].delete(tree, k)
else:
self.merge(tree, i - 1)
self.c[i - 2].delete(tree, k)
else:
self.c[i - 1].delete(tree, k)
def merge(self, tree, i):
y = self.c[i - 1]
z = self.c[i]
t = y.t
yn = y.n
zn = z.n
y.key[t - 1] = self.key[i - 1]
for j in range(1, zn + 1):
y.key[j + yn] = z.key[j - 1]
if not y.leaf:
for j in range(1, zn + 2):
y.c[j + yn] = z.c[j - 1]
y.n = yn + zn + 1
for j in range(i, self.n):
self.key[j - 1] = self.key[j]
for j in range(i + 1, self.n + 1):
self.c[j - 1] = self.c[j]
self.n = self.n - 1
if tree.root == self and self.n == 0:
tree.root = y
class BTree:
def __init__(self, t):
self.t = t
self.root = BTreeNode(t, True, 0)
def insert(self, k):
r = self.root
t = self.t
if r.n == 2 * t - 1:
s = BTreeNode(t, False, 0)
self.root = s
s.c[0] = r
s.split_child(1)
s.insert_nonfull(k)
else:
r.insert_nonfull(k)
def print_b_tree(self):
r = self.root
r.print_inorder()
# def predecessor(self, k):
# m = []
# x = self.root
# while not x.leaf:
# i = 1
# while i <= x.n and k > x.key[i - 1]:
# i = i + 1
# if i <= x.n and k == x.key[i - 1]:
# x = x.c[i - 1]
# while not x.leaf:
# x = x.c[x.n]
# return x.key[x.n - 1]
# else:
# x = x.c[i - 1]
# if i > 1:
# m.append(x.key[i - 1])
# i = 1
# while i <= x.n and k != x.key[i - 1]:
# i = i + 1
# if i > x.n or len(m) == 0:
# return None
# elif i > 1:
# return x.key[i - 2]
# else:
# return max(m)
def predecessor(self, k):
s = []
x = self.root
while True:
i = 1
while i <= x.n and k > x.key[i - 1]:
i = i + 1
if i > 1:
s.append(x.key[i - 2])
if x.leaf:
break
else:
x = x.c[i - 1]
if len(s) == 0:
return None
else:
return max(s)